Centroid dynamics with quantum statistics

Abstract

AbstractThis paper discusses the recent developments of a new molecular dynamics approach for the study of quantum dynamics for systems obeying Bose—Einstein statistics. The formalism is based on the mapping of a quantum mechanical system onto a set of phase space variables. These phase space variables are associated with the centroid (center‐of‐mass) of a Feynman path. We present the essential features of the formalism for the representation of operators and correlation functions and discuss some aspects of its practical implementation. We also present a recently developed simplified model for superfluid environments, based on an effective centroid potential approximation to the partition function. In the context of this model, we introduce a new expression for the calculation of the condensate fraction based on the off‐diagonal one‐particle density matrix. We perform calculations for a many‐particle system where the masses and pair interactions correspond to those of helium. The results show that this simplified model exhibits Bose—Einstein condensation below a certain characteristic temperature.